{
  "id": "1509.06435",
  "version": "v1",
  "published": "2015-09-22T00:53:38.000Z",
  "updated": "2015-09-22T00:53:38.000Z",
  "title": "Spectral analysis of stable processes on the positive half-line",
  "authors": [
    "Alexey Kuznetsov",
    "Mateusz Kwasnicki"
  ],
  "comment": "30 pages",
  "categories": [
    "math.PR",
    "math.FA",
    "math.SP"
  ],
  "abstract": "We study the spectral expansion of the semigroup of a general stable process killed on the first exit from the positive half-line. Starting with the Wiener-Hopf factorization we obtain the q-resolvent density for the killed process, from which we derive the spectral expansion of the semigroup via the inverse Laplace transform. The eigenfunctions and co-eigenfunctions are given rather explicitly in terms of the double sine function and they give rise to a pair of integral transforms which generalize the classical Fourier sine transform. Our results provide the first explicit example of a spectral expansion of the semigroup of a non-symmetric Levy process killed on the first exit form the positive half-line.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-09-22T00:53:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G52",
      "60J35"
    ],
    "keywords": [
      "positive half-line",
      "stable process",
      "spectral analysis",
      "spectral expansion",
      "inverse laplace transform"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150906435K"
    }
  }
}